Nguyen Van Liem Zhang Jianrun Jiao Renqiang

(1Hubei Key Laboratory of Intelligent Conveying Technology and Device, Hubei Polytechnic University, Huangshi 435003, China)(2School of Mechanical Engineering, Southeast University, Nanjing 211189, China)

Abstract：A design of different microtextures on the surface of the crankpin bearing(CB)is proposed to ameliorate the lubrication and friction performance(LFP)of engines.On the basis of the CB’s hydrodynamic lubrication model, the bearing surface of CB using different microtextures, such as wedge-shaped textures(WSTs), square textures(STs), circular textures(CTs), and combined square-circular textures(CSCTs), is simulated and assessed under various external loads of the CB at an engine speed of 2 000 r/min.The pressure of the oil film, the frictional force, the force of the solid asperity contact, and the friction coefficient of the CB are used as objective functions.Results indicate that the bearing surface designed by the STs remarkably improves the CB’s LFP in comparison with other structures of WSTs, CTs, and CSCTs.Particularly, the average values of the frictional force, solid asperity contact, and friction coefficient of the CB using the STs are greatly reduced by 28.5%, 14.5%, and 33.2% and by 34.4%, 26.3%, and 43.6% in comparison with the optimized CB dimensions and CTs, respectively.Therefore, the application of the STs on the CB surfaces can enhance the LFP of engines.

Key words：crankpin bearing; microtextures; lubrication and friction performance(LFP); texture

Studying the lubricating properties ofan engine’s crankpin bearings(CBs)to ameliorate the lubrication and friction performance(LFP)of engines is a topic of interest for many researchers.On the basis of the design parameters of an engine, the influence of the CB’s dimensions, such as the radius of the bearing and crankpin(rbandrc), the bearing width(B), the gap between the crankpin and bearing(c=rb-rc), and the CB’s surface roughness(σ)on the LFP, has been researched[1-5].The parameters ofrb,rc,B,c, andσof the CB were also optimized to enhance the CB’s LFP[6-8].Results indicated that the CB’s LFP was significantly ameliorated by the optimization of the CB’s dimensions.The investigations also emphasized that the friction force(Ff)and solid asperity contact force(Wac)generated in the elastic hydrodynamic lubrication(EHL)region of the CB with a minimum oil film thickness(ho)below 10 μm were still high[5, 8-9], particularly at the engine’s combustion stroke.Thus, to reduce theFfandWacand improve the LFP of the CB, thehoand the oil film pressure(p)in the EHL region should be increased.However, improvingpandhoby using only the parameters of the optimized CB is difficult.

To enhance thepandho, on the basis of research on microtextures added to the non-slip surface of friction pairs[10-14], an optimal design of the circular textures(CTs)of microtextures with a distribution density of {a×b}={6×6} was applied on the bearing surface to ameliorate the LFP[15].This approach enhanced not only thepandhobut also the CB’s LFP.However, the results of theFfandWacof the CB using the CTs{6×6} were still greater than that of the CB using the parameters ofrb,rc,B,c, andσoptimized in Ref.[8].Furthermore, the study used only one type of CTs{6×6}.The wedge-shaped textures(WSTs)and the square textures(STs)of the microtextures designed on the journal bearings also significantly affected the tribological properties of journal bearings but have not been a topic of concern so far.Thus, the effectiveness of the microtextures in improving the CB’s LFP has not been fully reflected yet.

On the basis of existing research on microtextures designed for friction pairs and journal bearings, the effect of the distribution density and shape of various microtextures, including CTs, STs, WSTs, circles-ellipses, and circles-triangles, on the lubrication performance was investigated[16-19].The results indicated that the microtextures could significantly affect the vibration and acoustics of contacting pairs[19].However, with a 5-20 μm depth of microtextures designed on the contacting pairs, theFfandWacwere remarkably reduced, especially with both the CTs and STs[17-18].Therefore, the CTs and STs of microtextures were designed and used on the bearing surface to ameliorate the friction and lubrication effectiveness of journal bearings[20-22].However, the external load(W0)that impacts the shaft, which greatly affected thepandhoin the EHL region of the journal bearings, was ignored or assumed to be constant in the above research.The influence of the microtextures of the WSTs, STs, and combined square-circular textures(CSCTs)on the CB’s LFP under the impact of a change inW0has not yet been fully researched and evaluated in existing research.

On the basis of the CB’s dimensions optimized in Ref.[8], the CTs of microtextures optimized in Ref.[15], and a hydrodynamic model of the CB, the above issues were elucidated by proposing and researching a design of different microtextures of the WSTs, STs, CTs, and CSCTs on the bearing surface to improve the LFP of engines under different external loads ofW0impacting on the crankpin at an engine speed of 2 000 r/min.Thep,Ff,Wac, and the friction coefficient(μ)of the CB are selected as the objective functions to evaluate the CB’s LFP.This study aims to assess the influence of various microtextures on enhancing the lubrication effectiveness and reducing the frictional power loss of engines.

1 Modeling of CB Lubrication and Microtextures

A CB hydrodynamic lubrication model supported by theW0is established in Fig.1(a)to assess the effect of various microtextures on ameliorating the CB’s LFP.To simplify the design process of the different microtextures on the bearing surface, the bearing surface modeled in the Cartesian counterpart[22]is applied to design the WSTs, STs, CTs, and CSCTs for improving thehoandp.The depth of all the textures is assumed to be the same, and the distance between each texture designed on the bearing surface is equidistant in thex-andy-directions, as shown in Fig.1(b).

(a)

In Fig.1,ω,φ, andψare the angular velocity, angular coordinate, and attitude angle of the crankpin in the bearing, respectively;eis the eccentricity between the shaft and bearing centers;Ris the radius of the CTs;Abis the area of the bearing surface;uis the moving velocity of the crankpin in the bearing;LxandLyare the bearing length and width, respectively;lxandlyare the dimensions of the texture surfaces;lsis the length and width of WSTs or STs; andhtis the maximum depth of WSTs, STs, and CTs, respectively.

Givenrc

According to the model of different microtextures designed on the bearing surface in Fig.1(b), the actual oil film thickness created bycandhtis written as

h=ht+ho=ht+c(1+εcosφ)

(1)

The mathematical equations of WSTs, STs, CTs, and CSCTs are presented below to determine the shape and thehtof different microtextures.

1.1 Wedge-shaped textures

On the basis of the design of WSTs in Fig.1(b), the relationshipslxandlybetween the WSTs andAbin thex-andy-directions are calculated by

(2)

whereaandbare the number of microtextures distributed in thex-andy-directions, respectively.

The shape equations of WSTs are given by

(3)

The depth equation of WSTs is written as

(4)

wherexiandyjare the coordinates of WSTs in thex-andy-directions,i=1,2,3,…,aandj=1,2,3,…,b.

1.2 Square textures

With the design of STs in the same Fig.1(b), the relationshipslxandlybetween STs andAbare calculated by Eq.(2), and the shape equations of STs are determined by Eq.(3).Herein,h=ho+ht, andhtis a constant.

Circular textures: On the basis of the structure of CTs in Fig.1(b), the relationshipslxandlybetween CTs andAbare calculated by

(5)

Thus, the equations of the shape and thehof CTs are

(6)

wherexi=(i-0.5)(lx+2R)andyj=(j-0.5)(ly+2R)are the CT center coordinates in thex-andy-directions, respectively, andht=Rc(1-cosα)is the depth of CTs.

1.3 Combined square-circular textures

On the basis of the CSCTs designed in Fig.1(d), the relationshipslxandlybetween CSCTs andAbin thex-andy-directions are written as

(7)

According to the shape and depth equations of STs and CTs calculated in Eqs.(3)and(6), the shape and depth equations of CSCTs could be rewritten as follows:

i=2a,j=2b-1

(8)

(9)

All the shape and depth equations of WSTs, STs, CTs, and CSCTs are then calculated and simulated by combining Eqs.(3),(6), and(8).

2 Application of Reynolds Equations

Reynolds equations were applied to compute thehandpof the friction pairs or journal bearings[5,23].In this study, the lubrication equations of the CB are computed under an actingW0on the crankpin, the CB’sσ, and the depth and structure of WSTs, STs, CTs, and CSCTs on the bearing surface.To perform the calculation, some assumptions of the model need to be given as follows: 1)The bearing surface is fixed, and the crankpin surface moves only on the bearing surface with a velocity ofu=rb×ωin thex-direction; 2)The oil film’s velocity in the centripetal motion and the inertia of the oil flow are very small; 3)The characteristics of the dynamic viscosity(η)and density of the oil film are unaltered during the CB’s operation.

Therefore, a general form of the Reynolds equations and a dimensionless form are given based on the CB’s hydrodynamic lubrication model as follows[8,15]:

(10)

(11)

whereαsand(αx,αy)are the factors of the pressure and shear flows;X=x/Lx;Y=y/Ly;γ=Lx/Ly;H=h/c;P=p/p0;Λ=6ηωLy2/(p0c2);Γ=12ηωLy2/(t0p0c2);T=t/t0;Δ=σ/c; andp0=101 325 Pa is the atmospheric pressure.

To calculate thepandhin Eq.(10), their boundary conditions need to be defined as follows: 1)halways exists and distributes over the bearing surface, 2)the maximum value ofhatφ=0° in Fig.1(a)is defined as the inlet oil film atmand outlet oil film atnin Fig.1(c), 3)the inlet and outlet pressures and the boundary pressures of the CB atm,n,g, andqin Fig.1(c)are defined by the samep0, and 4)thepcin the CB’s cavitation region is computed bypc=pswithp≤psandpc=pwithp>ps(psis the saturation pressure).Thus, the boundary pressures of the bearing surface are calculated byp(φ=0°)=p(φ=360°)=pandp(x=0)=p(x=B)=0, and both thehandpcan then be determined.

3 Evaluation Indexes of LFP

Under the actingW0on the crankpin, the load-bearing capacity of CB defined byW=Wof+Wacmust balance withW0to ensure the normal operation of CB.Consequently,pneeds to be increased to enhance the load-bearing capacityWofof the oil film.Concurrently, thepacgenerated in the EHL region needs to be decreased to reduce theFfandWacof CB[5,8].FfandWare strongly affected by bothpandh[3].Therefore, the different microtextures of WSTs, STs, CTs, and CSCTs are used to enhance thepandh, thereby improving the CB’s LFP.In assessing the influence of the different microtextures on ameliorating the LFP, the indexes of the increase ofpand the reduction ofFf,Wac, andμthat are selected as objective functions are then determined as follows:

1)Pressure distribution of the oil film.The oil film’s pressure distribution is determined in Eq.(10).

2)CB’s friction force.The friction forceFfgenerated in CB is determined by two friction forces that are generated due to the oil film motion and the solid contact of two CB surfaces in the EHL region.Thus,Ffis described as follows[7]:

Ff=?Ab(τac+τ)dxdy

(12)

whereτacandτare the asperity contact stress and interfacial shear stress of the CB surfaces, respectively.

(13)

4)CB’s friction coefficient.On the basis of the value ofFfdetermined by Eq.(12)andW0, theμof CB is then determined as follows[5,9]:

(14)

4 Simulation and Discussion

4.1 Computation of various microtextures

To compute the various microtextures of WSTs, STs, CTs, and CSCTs and to assess their effectiveness in ameliorating the CB’s LFP compared with the existing results of the CB parameters optimized in Ref.[8]and CTs{6×6} optimized in Ref.[15], the optimized CB parameters and optimized CTs{6×6} listed in Tab.1 are used as input parameters to simulate the results under theW0acting on the crankpin at a speed of 2 000 r/min(see Fig.2).

Fig.2 Data of W0 acting on the crankpin of CB

The research results of CTs in Ref.[24]showed that the distribution density of CTs{12×6} improves the tribological properties better than that of CTs{6×6}.Therefore, to compute and compare the effectiveness of the WSTs, STs, CTs, and CSCTs for ameliorating the CB’s LFP, the parameters of all the microtextures listed in Tab.1 are distributed on theAbof the CB as follows: 1)The matrix {a×b} of all microtextures distributed on theAbin thex-andy-directions is chosen bya=12 andb=6; 2)The CB’s length and width are defined byLx=2πrb=126.1 mm andLy=B=18.06 mm; 3)The radius of CTs and the length and width of WSTs or STs are defined byR=ls/2=0.85 mm; 4)The depth of all the microtextures is defined byht=5.5 μm.

Tab.1 Optimal parameters of CTs and CB

In accordance with the defined input parameters, the mathematical equations of the CB, and the determined microtextures, an algorithm program written in MATLAB is applied to calculate the objective functions under the same simulation condition.From the simulation results, the distribution densities of WSTs, STs, CTs, and CSCTs on theAbare indicated in Fig.3.The results in Fig.3 are then applied to compute and analyze thehandpand CB’s LFP.

(a)

4.2 Discussions

Theht=5.5 μm of WSTs, STs, CTs, and CSCTs is computed and indicated in Fig.4.Thehadded by thehtis then plotted in Fig.5.Fig.5 shows that thehis smaller than the safe oil film thickness in Ref.[5]at a range from 198° to 212° of the circumferential coordinate.This result could be due to the maximumW0acting on the crankpin at the combustion cycle of the engine.Therefore, theeof the CB is increased and thehis decreased.In the EHL region withh≤ 10 μm, both theFfandWaccould be strongly increased.Therefore, both thepandhin this region should be enhanced to ameliorate the CB’s LFP.

(a)

With theht=5.5 μm of all the microtextures added on the bearing surface, the result of thehin Fig.5 is also enhanced.Thus, thepis also increased in comparison to the condition without microtextures, especially in the EHL region, as shown in Fig.6.Fig.6 shows that the maximum values of thepwith the use of WSTs, STs, CTs, and CSCTs are 216.6, 224.7, 211.6, and 207.5 MPa, respectively.All their maximumpare substantially increased compared with that of 189.4 MPa without microtextures in Refs.[7-8].In addition, the comparison results of the maximumpwith the use of different microtextures show that STs have the highest maximump.This result is similar to the result of STs designed in journal bearings[13, 18].This finding means that both theFfandWacin the EHL region could be substantially ameliorated by STs.To clarify this argument, all theFf,Wac, andμare calculated and given in Figs.7(a),(b), and(c), respectively, on the basis of the simulation results ofhandpin Figs.4 and 5.

(a)

(a)

Tab.2 Average values of Ff, Wac, and μ

5 Conclusions

3)The contact of the crankpin and bearing surfaces always generates a friction force, which not only increases the frictional power loss but also decreases the CB durability of engines.Therefore, the CB surfaces designed by the STs could contribute to reducing the frictional power loss and increasing the durability of engines.

4)On the basis of the effectiveness of the STs in improving the CB’s LFP, these findings could also be applied to other journal bearings to enhance their lubrication performance and reduce their friction.